A003368 Numbers that are the sum of 12 positive 6th powers.

12, 75, 138, 201, 264, 327, 390, 453, 516, 579, 642, 705, 740, 768, 803, 866, 929, 992, 1055, 1118, 1181, 1244, 1307, 1370, 1433, 1468, 1531, 1594, 1657, 1720, 1783, 1846, 1909, 1972, 2035, 2098, 2196, 2259, 2322, 2385, 2448, 2511, 2574, 2637, 2700, 2763, 2924, 2987

Offset

1,1

Links

David A. Corneth, Table of n, a(n) for n = 1..10000 (first 1000 terms from T. D. Noe)

Example

From David A. Corneth, Aug 03 2020: (Start)
54710 is in the sequence as 54710 = 2^6 + 3^6 + 3^6 + 3^6 + 3^6 + 4^6 + 4^6 + 4^6 + 4^6 + 4^6 + 5^6 + 5^6.
94302 is in the sequence as 94302 = 1^6 + 1^6 + 1^6 + 1^6 + 1^6 + 2^6 + 2^6 + 2^6 + 2^6 + 3^6 + 6^6 + 6^6.
133585 is in the sequence as 133585 = 1^6 + 1^6 + 1^6 + 3^6 + 3^6 + 3^6 + 3^6 + 3^6 + 4^6 + 4^6 + 4^6 + 7^6. (End)

Mathematica

Module[{upto=2200, r}, r=Ceiling[Surd[upto, 6]]; Select[Union[Total/@ Tuples[ Range[r]^6, 12]], #<=upto&]] (* Harvey P. Dale, Aug 25 2015 *)

Prog

(PARI) (A003368_upto(N, k=12, m=6)=[n|n<-[1..#N=sum(n=1, sqrtnint(N, m), 'x^n^m, O('x^N))^k], polcoef(N, n)])(3000) \\ 2nd & 3rd optional arg allow to get other sequences of this group. See A003333 for alternate code. - M. F. Hasler, Aug 03 2020

Crossrefs

Cf. A001014 (sixth powers).

Cf. A003358 - A003367 (numbers that are the sum of 2, ..., 11 positive 6th powers); A003335, A003346, A003357, A003379, A003390, A004801, A004812, A004823 (numbers that are the sum of 12 positive 3rd, ..., 11th powers).

Sequence in context: A346446 A064121 A064116 * A246767 A328526 A092867

Adjacent sequences: A003365 A003366 A003367 * A003369 A003370 A003371

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved